A Structure Theorem for Quasi-hopf Bimodule Coalgebras
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چکیده
Let H be a quasi-Hopf algebra. We show that any H-bimodule coalgebra C for which there exists an H-bimodule coalgebra morphism ν : C → H is isomorphic to what we will call a smash product coalgebra. To this end, we use an explicit monoidal equivalence between the category of two-sided two-cosided Hopf modules over H and the category of left Yetter-Drinfeld modules over H. This categorical method allows also to reobtain the structure theorem for a quasi-Hopf (bi)comodule algebra given in [Panaite, Van Oystaeyen, 2007] and [Dello, Panaite, Van Oystaeyen, Zhang, 2016].
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تاریخ انتشار 2017